Shifts of position and changes of mind are personally hard for people because it involves a shift in personal identity. Constructivism and Realism are different in how they approach this. Constructivism, by its nature, might find it easier to appreciate multiple identities based on multiple constructs - but they are not immune from fundamentalism (for example, they might overly assert the 'implicit' ontology of constructivism and (ironically) insist on constructivism being real)... Realism on the other hand, by insisting on 'reality' can become more susceptible to fundamentalism. Personally, I don't think we can escape the fact that our identities (critical realists, constructivists, jedi...) are tied to positions and assertions of what's real and what isn't.
But how do we move forward? It strikes me that this must be a methodological development.. and more particularly one which takes account of diverse perspectives and diverse identities which are nonetheless 'real' (or at least part of a personal identity) to those who possess them (even the climate change deniers!). Establishing real mechanisms in it all must surely be a participative and appreciative exercise and not one where one set of distinctions (Bhaskar's, Latour's or anyone else's) holds sway. If Bhaskar is right and the reality behind individual perspectives can be revealed, the process of revealing it collaboratively can itself be transformative ("if you think climate change is not happening, what's your theory for what's going on when the ice-caps are melting?"... "what if you're wrong?"... etc.). But I think to make that work, an understanding of a real world must coexist with an understanding of ourselves as passionate, identity-seeking, distinction-making entities.